Simplest: Use the minicampaign setup. Either the Twin Shadows / The Bespin Gambit (3XP etc.) or Tyrants of Lothal (2XP etc.).
You can can also use "simulated" values to play side missions at any side mission slot: https://boardgamegeek.com/article/23060260#23060260
Also: https://community.fantasyflightgames.com/topic/220541-playing-one-off-side-missions/

Yes, she can use Battleship Leadership to waste an action. When resolving Battleship Leadership she cannot declare an attack while stunned, declaring an attack equals declaring a target, thus because there is no attack there is no target,the other friendly figure doesn't have a target for its attack, and thus the attack cannot be performed.

Right. When the attack was declared, the hero had less than 2 strain.
It would be different if No Quarter was instead: "When an Imperial figure declares an attack, if the target is a hero who has suffered 2 or more Strain, apply +1 Surge to the attack results", the trigger would be "when declaring an attack" and the ability would always trigger on imperial attacks, and the target and strain would be checked when the ability is resolved.

Performing an ability seems analogous to paying the cost to perform an ability - it doesn't cause the original trigger to be re-evaluated:
1. Declare a valid target (in line of sight)
if the target is hero who has suffered 2 or more strain, No Quarter triggers
if the target is a figure within 3 spaces, Relentless triggers.
If both No Quarter and Relentless triggered, they triggered at the same time and you can choose the order in which they are resolved.
If only Relentless triggers, it is performed.
If only No Quarter triggers, it is performed.
If neither trigger, neither is performed.

1.yes.
2.no, it's open information.
3.gaining influence is open information, and spending influence seems to be open information.
To purchase Agenda cards, the Imperial player shuffles the Agenda deck and secretly draws four of them.
He may purchase any of these cards by spending influence equal to the cards' costs.
* The Imperial player does not show his drawn Agenda cards to the heroes. Any cards he does not
purchase are shuffled back into the deck without being revealed.
* Most Agenda cards are immediately read aloud and resolved when purchased. The only exception is if
the card instructs the player to "keep this card secret." The Imperial player keeps the card and resolves
the effect when he plays it.

There is no two action attack limit. (Only two action(point)s per activation.) Heroes can perform any number of attacks during their activation or outside of it.
Swords Dance can be used (immediately) after any melee attack Shyla performs, doesn't even need to be during her activation.